nested <nes### [at] hotmailcom> wrote:

[snip]

>   does anyone know why the fourth component of the 4d normal can't be
zero?
>
> Michael


It's completely analogous to 3d with a plane positioned somewhere
and two coordinates (i.e. x and y) of a point on the plane given,
looking for the value of the third (z).

Distance of slice from origin:                 D

Normal to the slice in 4-space:               N = < Nx, Ny, Nz, Nw >
(is of unit length after parsing)

Point on surface of  fractal in 4-space:    P = < x, y, z, w >
(x, y, z are known; w is unknown)


For the point in 4d to be an element of the slice subspace
the vectors have to satisfy the equation:

P*N = D   --->   x*Nx + y*Ny + z*Nz + w*Nw = D,

and

w = (D - x*Nx - y*Ny - z*Nz) / Nw

That's why Nw can't be zero...

Sorry for the late answer ( I hope it's not overlooked )

Gerald
ger### [at] aonat

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